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pythonnumpymatrix-multiplication
Mostafa Hosseini
Mostafa Hosseini

Reputation: 35

Matrix Multiplication 2-D and 1-D

Example:

import numpy as np

x = np.array([[1., 2., 3.], [4., 5., 6.]])
y = np.ones(3)

np.dot(x , y)

Result:

array([ 6., 15.])

How is this possible when I have a matrix of (2x3) by (1x3)? It should be a 3x1 matrix.

Upvotes: -2

Views: 94

Answers (3)

sjking
sjking

Reputation: 1290

You are taking the dot product of a 2D array and a 1D array (or vector) here. In numpy there is no distinction between row and column vectors. So in your example the vector is treated as a column vector. See here for more information.

Upvotes: 0

mozway
mozway

Reputation: 262214

In a dot product, the length of the last dimension of the left-side array should be identical to the length of the second-to-last dimension of the right-side array.

You can transpose y, if this makes sense in terms of your computation:

y = np.ones(shape=(1, 3))

out = np.dot(x , y.T)

Output:

array([[ 6.],
       [15.]])

Or convert back to 1D:

out = np.dot(x , y[0])

# or
out = np.dot(x , y.squeeze())

Output: array([ 6., 15.])

Upvotes: 0

fulvius
fulvius

Reputation: 56

y is not a 1x3 matrix but a 1-D vector (check y.size if in doubt). If you have a look at the documentation you can find

If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.

That's why it is returning a 1-D vector of two elements.

Upvotes: 3

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